EPSRC Reference: 
EP/G020809/1 
Title: 
Representation theory of finite Walgebras 
Principal Investigator: 
Goodwin, Professor SM 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics 
Organisation: 
University of Birmingham 
Scheme: 
First Grant Scheme 
Starts: 
17 August 2009 
Ends: 
16 August 2012 
Value (£): 
324,820

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
04 Sep 2008

Mathematics Prioritisation Panel

Deferred

03 Dec 2008

Mathematics Prioritisation Panel

Announced


Summary on Grant Application Form 
Recently there has been a great deal of interest in finite Walgebras and their representation theory from world leading mathematicians. This is largely due to connections to the representation theory and geometry of finite dimensional reductive Lie algebras. Finite Walgebras and their affine counterparts have also attracted much interest in mathematical physics motivated by their occurrence as nonlinear symmetry algebras in conformal field theory. The purpose of this research is to make significant advances in the representation theory of finite Walgebras and in particular to resolve the important problem of classifying finite dimensional simple modules.In recent joint work Brundan, Kleshchev and the author, have developed a highest weight theory for finite Walgebras. This leads to a natural strategy for tackling the problem of classifying finite dimensional simple modules, in analogy with the situation for complex reductive Lie algebras. The primary aim of this proposal is to successfully follow this strategy. The recent developments in the area of finite Walgebras and the diverse areas of mathematics feeding in to their representation theory will allow us to employ a variety of techniques in achieving this goal. In particular, we intend to exploit the interplay between the three equivalent definitions of a finite Walgebra: the Whittaker model definition, the definition via quantum Hamiltonian reduction, and the definition via Fedosov reduction. In addition to our main objective, there are a number of other important problems concerning the representation theory of finite Walgebras that we will investigate.

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Date Materialised 


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Further Information: 

Organisation Website: 
http://www.bham.ac.uk 